Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 15 Aug 2010 13:34:13 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/15/t1281879218q17g9ugb8huqey9.htm/, Retrieved Sun, 28 Apr 2024 04:31:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78863, Retrieved Sun, 28 Apr 2024 04:31:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSebastien Delforge
Estimated Impact143
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2010-08-15 13:34:13] [923770d86edf74ed976a539eae527e37] [Current]
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Dataseries X:
75
74
73
71
91
90
75
65
66
66
67
69
75
79
75
77
100
100
94
83
83
83
84
88
89
98
94
84
111
98
98
83
79
78
80
94
98
104
94
90
115
104
114
99
96
98
104
111
117
125
117
118
151
145
155
133
124
125
131
133
136
141
130
137
177
183
191
166
156
153
164
164
168
173
164
165
205
207
215
190
169
175
188
188
196
201
194
197
237
236
244
222
195
199
207
204
212
222
214
217
258
256
251
223
198
206
214
212
227
238
228
235
275
278
278
251
225
232
238
239




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78863&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78863&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78863&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.582467316896955
beta0.00891834531619204
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.582467316896955 \tabularnewline
beta & 0.00891834531619204 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78863&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.582467316896955[/C][/ROW]
[ROW][C]beta[/C][C]0.00891834531619204[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78863&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78863&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.582467316896955
beta0.00891834531619204
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137571.5791174702093.42088252979096
147977.04174296496071.95825703503931
157573.87511025845851.12488974154145
167776.20551248570650.794487514293508
1710099.17248847702310.827511522976863
1810099.16911290350150.830887096498472
199486.82506687463147.17493312536855
208379.64024674372013.3597532562799
218383.547765386508-0.547765386508033
228383.8698614938643-0.869861493864306
238484.9372723263794-0.937272326379414
248887.03323293492510.966767065074876
258996.6679258409937-7.66792584099373
269895.49109266685682.50890733314324
279491.04089711938952.95910288061047
288494.4670000951766-10.4670000951766
29111114.002231882253-3.00223188225321
3098111.515075359236-13.5150753592364
319892.81167592303735.18832407696266
328382.47769951088910.52230048911089
337982.995508253576-3.99550825357606
347881.0633203144457-3.06332031444572
358080.6627344700765-0.662734470076529
369483.46638643580810.5336135641920
379894.89703856191553.10296143808446
38104104.739779441506-0.739779441506158
399498.069994250363-4.06999425036301
409091.3143922810225-1.31439228102251
41115121.363623452776-6.36362345277631
42104111.628450526258-7.62845052625785
43114103.66537714940110.3346228505994
449992.43459996256166.56540003743835
459694.14018026103631.85981973896368
469896.00492107418561.99507892581435
47104100.0005357700013.99946422999894
48111111.851768129400-0.851768129399588
49117113.7864731350193.21352686498066
50125123.1029469230991.89705307690106
51117114.9135410721802.08645892781986
52118111.9968201211696.00317987883086
53151152.048150724256-1.04815072425623
54145142.4625688117542.53743118824551
55155148.9436300740486.05636992595183
56133127.0075570262115.9924429737887
57124124.972449397232-0.972449397231827
58125125.350525044817-0.350525044816536
59131129.6554800300221.34451996997751
60133139.703546686813-6.7035466868129
61136140.687307443733-4.68730744373258
62141145.939995819250-4.93999581924956
63130132.380154852621-2.38015485262147
64137127.9940010895789.00599891042238
65177171.0379583763275.96204162367269
66183165.71458428869217.2854157113084
67191183.4136725712527.58632742874761
68166156.7428932544859.25710674551544
69156151.7425668950544.25743310494568
70153155.612386256077-2.61238625607706
71164160.4071964454083.59280355459228
72164169.611598706644-5.61159870664358
73168173.346368825837-5.346368825837
74173179.921105711391-6.92110571139114
75164163.7744304568260.225569543173833
76165165.823052935499-0.823052935498822
77205209.226785901903-4.22678590190284
78207201.3887141605935.61128583940683
79215208.4300033503386.5699966496615
80190178.21572443912211.7842755608785
81169171.021462214153-2.02146221415273
82175168.1097141857536.89028581424708
83188182.0103310400535.98966895994653
84188189.033257888467-1.03325788846652
85196196.448183339317-0.448183339317040
86201206.546299973469-5.54629997346905
87194192.4831848740361.51681512596366
88197195.0104817497471.98951825025298
89237246.507635701937-9.50763570193737
90236239.313466768335-3.31346676833502
91244241.9814393520662.01856064793424
92222206.7996019473515.2003980526502
93195193.0481495206511.95185047934939
94199196.2954227925572.70457720744298
95207208.467525120273-1.46752512027308
96204208.164704095828-4.16470409582845
97212214.661651522177-2.66165152217744
98222221.8974011948900.10259880510975
99214213.1382301074850.861769892514872
100217215.5516771571621.44832284283794
101258266.180957549843-8.18095754984313
102256262.297655250605-6.29765525060452
103251265.966797634245-14.9667976342448
104223224.309114938151-1.30911493815077
105198195.0728156105042.92718438949615
106206199.0807991116616.91920088833854
107214212.0127446602101.98725533978958
108212212.431008420139-0.431008420138539
109227221.9790804050855.02091959491511
110238235.3299199062292.67008009377139
111228227.7027359634540.297264036545982
112235230.0595367862224.94046321377769
113275281.870930309566-6.87093030956606
114278279.503066021618-1.50306602161754
115278282.328962909445-4.32896290944456
116251249.3574581061181.64254189388222
117225220.2573628977084.74263710229155
118232227.359534053414.6404659465901
119238237.6252458163830.374754183617227
120239235.8240671545343.17593284546595

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 75 & 71.579117470209 & 3.42088252979096 \tabularnewline
14 & 79 & 77.0417429649607 & 1.95825703503931 \tabularnewline
15 & 75 & 73.8751102584585 & 1.12488974154145 \tabularnewline
16 & 77 & 76.2055124857065 & 0.794487514293508 \tabularnewline
17 & 100 & 99.1724884770231 & 0.827511522976863 \tabularnewline
18 & 100 & 99.1691129035015 & 0.830887096498472 \tabularnewline
19 & 94 & 86.8250668746314 & 7.17493312536855 \tabularnewline
20 & 83 & 79.6402467437201 & 3.3597532562799 \tabularnewline
21 & 83 & 83.547765386508 & -0.547765386508033 \tabularnewline
22 & 83 & 83.8698614938643 & -0.869861493864306 \tabularnewline
23 & 84 & 84.9372723263794 & -0.937272326379414 \tabularnewline
24 & 88 & 87.0332329349251 & 0.966767065074876 \tabularnewline
25 & 89 & 96.6679258409937 & -7.66792584099373 \tabularnewline
26 & 98 & 95.4910926668568 & 2.50890733314324 \tabularnewline
27 & 94 & 91.0408971193895 & 2.95910288061047 \tabularnewline
28 & 84 & 94.4670000951766 & -10.4670000951766 \tabularnewline
29 & 111 & 114.002231882253 & -3.00223188225321 \tabularnewline
30 & 98 & 111.515075359236 & -13.5150753592364 \tabularnewline
31 & 98 & 92.8116759230373 & 5.18832407696266 \tabularnewline
32 & 83 & 82.4776995108891 & 0.52230048911089 \tabularnewline
33 & 79 & 82.995508253576 & -3.99550825357606 \tabularnewline
34 & 78 & 81.0633203144457 & -3.06332031444572 \tabularnewline
35 & 80 & 80.6627344700765 & -0.662734470076529 \tabularnewline
36 & 94 & 83.466386435808 & 10.5336135641920 \tabularnewline
37 & 98 & 94.8970385619155 & 3.10296143808446 \tabularnewline
38 & 104 & 104.739779441506 & -0.739779441506158 \tabularnewline
39 & 94 & 98.069994250363 & -4.06999425036301 \tabularnewline
40 & 90 & 91.3143922810225 & -1.31439228102251 \tabularnewline
41 & 115 & 121.363623452776 & -6.36362345277631 \tabularnewline
42 & 104 & 111.628450526258 & -7.62845052625785 \tabularnewline
43 & 114 & 103.665377149401 & 10.3346228505994 \tabularnewline
44 & 99 & 92.4345999625616 & 6.56540003743835 \tabularnewline
45 & 96 & 94.1401802610363 & 1.85981973896368 \tabularnewline
46 & 98 & 96.0049210741856 & 1.99507892581435 \tabularnewline
47 & 104 & 100.000535770001 & 3.99946422999894 \tabularnewline
48 & 111 & 111.851768129400 & -0.851768129399588 \tabularnewline
49 & 117 & 113.786473135019 & 3.21352686498066 \tabularnewline
50 & 125 & 123.102946923099 & 1.89705307690106 \tabularnewline
51 & 117 & 114.913541072180 & 2.08645892781986 \tabularnewline
52 & 118 & 111.996820121169 & 6.00317987883086 \tabularnewline
53 & 151 & 152.048150724256 & -1.04815072425623 \tabularnewline
54 & 145 & 142.462568811754 & 2.53743118824551 \tabularnewline
55 & 155 & 148.943630074048 & 6.05636992595183 \tabularnewline
56 & 133 & 127.007557026211 & 5.9924429737887 \tabularnewline
57 & 124 & 124.972449397232 & -0.972449397231827 \tabularnewline
58 & 125 & 125.350525044817 & -0.350525044816536 \tabularnewline
59 & 131 & 129.655480030022 & 1.34451996997751 \tabularnewline
60 & 133 & 139.703546686813 & -6.7035466868129 \tabularnewline
61 & 136 & 140.687307443733 & -4.68730744373258 \tabularnewline
62 & 141 & 145.939995819250 & -4.93999581924956 \tabularnewline
63 & 130 & 132.380154852621 & -2.38015485262147 \tabularnewline
64 & 137 & 127.994001089578 & 9.00599891042238 \tabularnewline
65 & 177 & 171.037958376327 & 5.96204162367269 \tabularnewline
66 & 183 & 165.714584288692 & 17.2854157113084 \tabularnewline
67 & 191 & 183.413672571252 & 7.58632742874761 \tabularnewline
68 & 166 & 156.742893254485 & 9.25710674551544 \tabularnewline
69 & 156 & 151.742566895054 & 4.25743310494568 \tabularnewline
70 & 153 & 155.612386256077 & -2.61238625607706 \tabularnewline
71 & 164 & 160.407196445408 & 3.59280355459228 \tabularnewline
72 & 164 & 169.611598706644 & -5.61159870664358 \tabularnewline
73 & 168 & 173.346368825837 & -5.346368825837 \tabularnewline
74 & 173 & 179.921105711391 & -6.92110571139114 \tabularnewline
75 & 164 & 163.774430456826 & 0.225569543173833 \tabularnewline
76 & 165 & 165.823052935499 & -0.823052935498822 \tabularnewline
77 & 205 & 209.226785901903 & -4.22678590190284 \tabularnewline
78 & 207 & 201.388714160593 & 5.61128583940683 \tabularnewline
79 & 215 & 208.430003350338 & 6.5699966496615 \tabularnewline
80 & 190 & 178.215724439122 & 11.7842755608785 \tabularnewline
81 & 169 & 171.021462214153 & -2.02146221415273 \tabularnewline
82 & 175 & 168.109714185753 & 6.89028581424708 \tabularnewline
83 & 188 & 182.010331040053 & 5.98966895994653 \tabularnewline
84 & 188 & 189.033257888467 & -1.03325788846652 \tabularnewline
85 & 196 & 196.448183339317 & -0.448183339317040 \tabularnewline
86 & 201 & 206.546299973469 & -5.54629997346905 \tabularnewline
87 & 194 & 192.483184874036 & 1.51681512596366 \tabularnewline
88 & 197 & 195.010481749747 & 1.98951825025298 \tabularnewline
89 & 237 & 246.507635701937 & -9.50763570193737 \tabularnewline
90 & 236 & 239.313466768335 & -3.31346676833502 \tabularnewline
91 & 244 & 241.981439352066 & 2.01856064793424 \tabularnewline
92 & 222 & 206.79960194735 & 15.2003980526502 \tabularnewline
93 & 195 & 193.048149520651 & 1.95185047934939 \tabularnewline
94 & 199 & 196.295422792557 & 2.70457720744298 \tabularnewline
95 & 207 & 208.467525120273 & -1.46752512027308 \tabularnewline
96 & 204 & 208.164704095828 & -4.16470409582845 \tabularnewline
97 & 212 & 214.661651522177 & -2.66165152217744 \tabularnewline
98 & 222 & 221.897401194890 & 0.10259880510975 \tabularnewline
99 & 214 & 213.138230107485 & 0.861769892514872 \tabularnewline
100 & 217 & 215.551677157162 & 1.44832284283794 \tabularnewline
101 & 258 & 266.180957549843 & -8.18095754984313 \tabularnewline
102 & 256 & 262.297655250605 & -6.29765525060452 \tabularnewline
103 & 251 & 265.966797634245 & -14.9667976342448 \tabularnewline
104 & 223 & 224.309114938151 & -1.30911493815077 \tabularnewline
105 & 198 & 195.072815610504 & 2.92718438949615 \tabularnewline
106 & 206 & 199.080799111661 & 6.91920088833854 \tabularnewline
107 & 214 & 212.012744660210 & 1.98725533978958 \tabularnewline
108 & 212 & 212.431008420139 & -0.431008420138539 \tabularnewline
109 & 227 & 221.979080405085 & 5.02091959491511 \tabularnewline
110 & 238 & 235.329919906229 & 2.67008009377139 \tabularnewline
111 & 228 & 227.702735963454 & 0.297264036545982 \tabularnewline
112 & 235 & 230.059536786222 & 4.94046321377769 \tabularnewline
113 & 275 & 281.870930309566 & -6.87093030956606 \tabularnewline
114 & 278 & 279.503066021618 & -1.50306602161754 \tabularnewline
115 & 278 & 282.328962909445 & -4.32896290944456 \tabularnewline
116 & 251 & 249.357458106118 & 1.64254189388222 \tabularnewline
117 & 225 & 220.257362897708 & 4.74263710229155 \tabularnewline
118 & 232 & 227.35953405341 & 4.6404659465901 \tabularnewline
119 & 238 & 237.625245816383 & 0.374754183617227 \tabularnewline
120 & 239 & 235.824067154534 & 3.17593284546595 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78863&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]75[/C][C]71.579117470209[/C][C]3.42088252979096[/C][/ROW]
[ROW][C]14[/C][C]79[/C][C]77.0417429649607[/C][C]1.95825703503931[/C][/ROW]
[ROW][C]15[/C][C]75[/C][C]73.8751102584585[/C][C]1.12488974154145[/C][/ROW]
[ROW][C]16[/C][C]77[/C][C]76.2055124857065[/C][C]0.794487514293508[/C][/ROW]
[ROW][C]17[/C][C]100[/C][C]99.1724884770231[/C][C]0.827511522976863[/C][/ROW]
[ROW][C]18[/C][C]100[/C][C]99.1691129035015[/C][C]0.830887096498472[/C][/ROW]
[ROW][C]19[/C][C]94[/C][C]86.8250668746314[/C][C]7.17493312536855[/C][/ROW]
[ROW][C]20[/C][C]83[/C][C]79.6402467437201[/C][C]3.3597532562799[/C][/ROW]
[ROW][C]21[/C][C]83[/C][C]83.547765386508[/C][C]-0.547765386508033[/C][/ROW]
[ROW][C]22[/C][C]83[/C][C]83.8698614938643[/C][C]-0.869861493864306[/C][/ROW]
[ROW][C]23[/C][C]84[/C][C]84.9372723263794[/C][C]-0.937272326379414[/C][/ROW]
[ROW][C]24[/C][C]88[/C][C]87.0332329349251[/C][C]0.966767065074876[/C][/ROW]
[ROW][C]25[/C][C]89[/C][C]96.6679258409937[/C][C]-7.66792584099373[/C][/ROW]
[ROW][C]26[/C][C]98[/C][C]95.4910926668568[/C][C]2.50890733314324[/C][/ROW]
[ROW][C]27[/C][C]94[/C][C]91.0408971193895[/C][C]2.95910288061047[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]94.4670000951766[/C][C]-10.4670000951766[/C][/ROW]
[ROW][C]29[/C][C]111[/C][C]114.002231882253[/C][C]-3.00223188225321[/C][/ROW]
[ROW][C]30[/C][C]98[/C][C]111.515075359236[/C][C]-13.5150753592364[/C][/ROW]
[ROW][C]31[/C][C]98[/C][C]92.8116759230373[/C][C]5.18832407696266[/C][/ROW]
[ROW][C]32[/C][C]83[/C][C]82.4776995108891[/C][C]0.52230048911089[/C][/ROW]
[ROW][C]33[/C][C]79[/C][C]82.995508253576[/C][C]-3.99550825357606[/C][/ROW]
[ROW][C]34[/C][C]78[/C][C]81.0633203144457[/C][C]-3.06332031444572[/C][/ROW]
[ROW][C]35[/C][C]80[/C][C]80.6627344700765[/C][C]-0.662734470076529[/C][/ROW]
[ROW][C]36[/C][C]94[/C][C]83.466386435808[/C][C]10.5336135641920[/C][/ROW]
[ROW][C]37[/C][C]98[/C][C]94.8970385619155[/C][C]3.10296143808446[/C][/ROW]
[ROW][C]38[/C][C]104[/C][C]104.739779441506[/C][C]-0.739779441506158[/C][/ROW]
[ROW][C]39[/C][C]94[/C][C]98.069994250363[/C][C]-4.06999425036301[/C][/ROW]
[ROW][C]40[/C][C]90[/C][C]91.3143922810225[/C][C]-1.31439228102251[/C][/ROW]
[ROW][C]41[/C][C]115[/C][C]121.363623452776[/C][C]-6.36362345277631[/C][/ROW]
[ROW][C]42[/C][C]104[/C][C]111.628450526258[/C][C]-7.62845052625785[/C][/ROW]
[ROW][C]43[/C][C]114[/C][C]103.665377149401[/C][C]10.3346228505994[/C][/ROW]
[ROW][C]44[/C][C]99[/C][C]92.4345999625616[/C][C]6.56540003743835[/C][/ROW]
[ROW][C]45[/C][C]96[/C][C]94.1401802610363[/C][C]1.85981973896368[/C][/ROW]
[ROW][C]46[/C][C]98[/C][C]96.0049210741856[/C][C]1.99507892581435[/C][/ROW]
[ROW][C]47[/C][C]104[/C][C]100.000535770001[/C][C]3.99946422999894[/C][/ROW]
[ROW][C]48[/C][C]111[/C][C]111.851768129400[/C][C]-0.851768129399588[/C][/ROW]
[ROW][C]49[/C][C]117[/C][C]113.786473135019[/C][C]3.21352686498066[/C][/ROW]
[ROW][C]50[/C][C]125[/C][C]123.102946923099[/C][C]1.89705307690106[/C][/ROW]
[ROW][C]51[/C][C]117[/C][C]114.913541072180[/C][C]2.08645892781986[/C][/ROW]
[ROW][C]52[/C][C]118[/C][C]111.996820121169[/C][C]6.00317987883086[/C][/ROW]
[ROW][C]53[/C][C]151[/C][C]152.048150724256[/C][C]-1.04815072425623[/C][/ROW]
[ROW][C]54[/C][C]145[/C][C]142.462568811754[/C][C]2.53743118824551[/C][/ROW]
[ROW][C]55[/C][C]155[/C][C]148.943630074048[/C][C]6.05636992595183[/C][/ROW]
[ROW][C]56[/C][C]133[/C][C]127.007557026211[/C][C]5.9924429737887[/C][/ROW]
[ROW][C]57[/C][C]124[/C][C]124.972449397232[/C][C]-0.972449397231827[/C][/ROW]
[ROW][C]58[/C][C]125[/C][C]125.350525044817[/C][C]-0.350525044816536[/C][/ROW]
[ROW][C]59[/C][C]131[/C][C]129.655480030022[/C][C]1.34451996997751[/C][/ROW]
[ROW][C]60[/C][C]133[/C][C]139.703546686813[/C][C]-6.7035466868129[/C][/ROW]
[ROW][C]61[/C][C]136[/C][C]140.687307443733[/C][C]-4.68730744373258[/C][/ROW]
[ROW][C]62[/C][C]141[/C][C]145.939995819250[/C][C]-4.93999581924956[/C][/ROW]
[ROW][C]63[/C][C]130[/C][C]132.380154852621[/C][C]-2.38015485262147[/C][/ROW]
[ROW][C]64[/C][C]137[/C][C]127.994001089578[/C][C]9.00599891042238[/C][/ROW]
[ROW][C]65[/C][C]177[/C][C]171.037958376327[/C][C]5.96204162367269[/C][/ROW]
[ROW][C]66[/C][C]183[/C][C]165.714584288692[/C][C]17.2854157113084[/C][/ROW]
[ROW][C]67[/C][C]191[/C][C]183.413672571252[/C][C]7.58632742874761[/C][/ROW]
[ROW][C]68[/C][C]166[/C][C]156.742893254485[/C][C]9.25710674551544[/C][/ROW]
[ROW][C]69[/C][C]156[/C][C]151.742566895054[/C][C]4.25743310494568[/C][/ROW]
[ROW][C]70[/C][C]153[/C][C]155.612386256077[/C][C]-2.61238625607706[/C][/ROW]
[ROW][C]71[/C][C]164[/C][C]160.407196445408[/C][C]3.59280355459228[/C][/ROW]
[ROW][C]72[/C][C]164[/C][C]169.611598706644[/C][C]-5.61159870664358[/C][/ROW]
[ROW][C]73[/C][C]168[/C][C]173.346368825837[/C][C]-5.346368825837[/C][/ROW]
[ROW][C]74[/C][C]173[/C][C]179.921105711391[/C][C]-6.92110571139114[/C][/ROW]
[ROW][C]75[/C][C]164[/C][C]163.774430456826[/C][C]0.225569543173833[/C][/ROW]
[ROW][C]76[/C][C]165[/C][C]165.823052935499[/C][C]-0.823052935498822[/C][/ROW]
[ROW][C]77[/C][C]205[/C][C]209.226785901903[/C][C]-4.22678590190284[/C][/ROW]
[ROW][C]78[/C][C]207[/C][C]201.388714160593[/C][C]5.61128583940683[/C][/ROW]
[ROW][C]79[/C][C]215[/C][C]208.430003350338[/C][C]6.5699966496615[/C][/ROW]
[ROW][C]80[/C][C]190[/C][C]178.215724439122[/C][C]11.7842755608785[/C][/ROW]
[ROW][C]81[/C][C]169[/C][C]171.021462214153[/C][C]-2.02146221415273[/C][/ROW]
[ROW][C]82[/C][C]175[/C][C]168.109714185753[/C][C]6.89028581424708[/C][/ROW]
[ROW][C]83[/C][C]188[/C][C]182.010331040053[/C][C]5.98966895994653[/C][/ROW]
[ROW][C]84[/C][C]188[/C][C]189.033257888467[/C][C]-1.03325788846652[/C][/ROW]
[ROW][C]85[/C][C]196[/C][C]196.448183339317[/C][C]-0.448183339317040[/C][/ROW]
[ROW][C]86[/C][C]201[/C][C]206.546299973469[/C][C]-5.54629997346905[/C][/ROW]
[ROW][C]87[/C][C]194[/C][C]192.483184874036[/C][C]1.51681512596366[/C][/ROW]
[ROW][C]88[/C][C]197[/C][C]195.010481749747[/C][C]1.98951825025298[/C][/ROW]
[ROW][C]89[/C][C]237[/C][C]246.507635701937[/C][C]-9.50763570193737[/C][/ROW]
[ROW][C]90[/C][C]236[/C][C]239.313466768335[/C][C]-3.31346676833502[/C][/ROW]
[ROW][C]91[/C][C]244[/C][C]241.981439352066[/C][C]2.01856064793424[/C][/ROW]
[ROW][C]92[/C][C]222[/C][C]206.79960194735[/C][C]15.2003980526502[/C][/ROW]
[ROW][C]93[/C][C]195[/C][C]193.048149520651[/C][C]1.95185047934939[/C][/ROW]
[ROW][C]94[/C][C]199[/C][C]196.295422792557[/C][C]2.70457720744298[/C][/ROW]
[ROW][C]95[/C][C]207[/C][C]208.467525120273[/C][C]-1.46752512027308[/C][/ROW]
[ROW][C]96[/C][C]204[/C][C]208.164704095828[/C][C]-4.16470409582845[/C][/ROW]
[ROW][C]97[/C][C]212[/C][C]214.661651522177[/C][C]-2.66165152217744[/C][/ROW]
[ROW][C]98[/C][C]222[/C][C]221.897401194890[/C][C]0.10259880510975[/C][/ROW]
[ROW][C]99[/C][C]214[/C][C]213.138230107485[/C][C]0.861769892514872[/C][/ROW]
[ROW][C]100[/C][C]217[/C][C]215.551677157162[/C][C]1.44832284283794[/C][/ROW]
[ROW][C]101[/C][C]258[/C][C]266.180957549843[/C][C]-8.18095754984313[/C][/ROW]
[ROW][C]102[/C][C]256[/C][C]262.297655250605[/C][C]-6.29765525060452[/C][/ROW]
[ROW][C]103[/C][C]251[/C][C]265.966797634245[/C][C]-14.9667976342448[/C][/ROW]
[ROW][C]104[/C][C]223[/C][C]224.309114938151[/C][C]-1.30911493815077[/C][/ROW]
[ROW][C]105[/C][C]198[/C][C]195.072815610504[/C][C]2.92718438949615[/C][/ROW]
[ROW][C]106[/C][C]206[/C][C]199.080799111661[/C][C]6.91920088833854[/C][/ROW]
[ROW][C]107[/C][C]214[/C][C]212.012744660210[/C][C]1.98725533978958[/C][/ROW]
[ROW][C]108[/C][C]212[/C][C]212.431008420139[/C][C]-0.431008420138539[/C][/ROW]
[ROW][C]109[/C][C]227[/C][C]221.979080405085[/C][C]5.02091959491511[/C][/ROW]
[ROW][C]110[/C][C]238[/C][C]235.329919906229[/C][C]2.67008009377139[/C][/ROW]
[ROW][C]111[/C][C]228[/C][C]227.702735963454[/C][C]0.297264036545982[/C][/ROW]
[ROW][C]112[/C][C]235[/C][C]230.059536786222[/C][C]4.94046321377769[/C][/ROW]
[ROW][C]113[/C][C]275[/C][C]281.870930309566[/C][C]-6.87093030956606[/C][/ROW]
[ROW][C]114[/C][C]278[/C][C]279.503066021618[/C][C]-1.50306602161754[/C][/ROW]
[ROW][C]115[/C][C]278[/C][C]282.328962909445[/C][C]-4.32896290944456[/C][/ROW]
[ROW][C]116[/C][C]251[/C][C]249.357458106118[/C][C]1.64254189388222[/C][/ROW]
[ROW][C]117[/C][C]225[/C][C]220.257362897708[/C][C]4.74263710229155[/C][/ROW]
[ROW][C]118[/C][C]232[/C][C]227.35953405341[/C][C]4.6404659465901[/C][/ROW]
[ROW][C]119[/C][C]238[/C][C]237.625245816383[/C][C]0.374754183617227[/C][/ROW]
[ROW][C]120[/C][C]239[/C][C]235.824067154534[/C][C]3.17593284546595[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78863&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78863&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137571.5791174702093.42088252979096
147977.04174296496071.95825703503931
157573.87511025845851.12488974154145
167776.20551248570650.794487514293508
1710099.17248847702310.827511522976863
1810099.16911290350150.830887096498472
199486.82506687463147.17493312536855
208379.64024674372013.3597532562799
218383.547765386508-0.547765386508033
228383.8698614938643-0.869861493864306
238484.9372723263794-0.937272326379414
248887.03323293492510.966767065074876
258996.6679258409937-7.66792584099373
269895.49109266685682.50890733314324
279491.04089711938952.95910288061047
288494.4670000951766-10.4670000951766
29111114.002231882253-3.00223188225321
3098111.515075359236-13.5150753592364
319892.81167592303735.18832407696266
328382.47769951088910.52230048911089
337982.995508253576-3.99550825357606
347881.0633203144457-3.06332031444572
358080.6627344700765-0.662734470076529
369483.46638643580810.5336135641920
379894.89703856191553.10296143808446
38104104.739779441506-0.739779441506158
399498.069994250363-4.06999425036301
409091.3143922810225-1.31439228102251
41115121.363623452776-6.36362345277631
42104111.628450526258-7.62845052625785
43114103.66537714940110.3346228505994
449992.43459996256166.56540003743835
459694.14018026103631.85981973896368
469896.00492107418561.99507892581435
47104100.0005357700013.99946422999894
48111111.851768129400-0.851768129399588
49117113.7864731350193.21352686498066
50125123.1029469230991.89705307690106
51117114.9135410721802.08645892781986
52118111.9968201211696.00317987883086
53151152.048150724256-1.04815072425623
54145142.4625688117542.53743118824551
55155148.9436300740486.05636992595183
56133127.0075570262115.9924429737887
57124124.972449397232-0.972449397231827
58125125.350525044817-0.350525044816536
59131129.6554800300221.34451996997751
60133139.703546686813-6.7035466868129
61136140.687307443733-4.68730744373258
62141145.939995819250-4.93999581924956
63130132.380154852621-2.38015485262147
64137127.9940010895789.00599891042238
65177171.0379583763275.96204162367269
66183165.71458428869217.2854157113084
67191183.4136725712527.58632742874761
68166156.7428932544859.25710674551544
69156151.7425668950544.25743310494568
70153155.612386256077-2.61238625607706
71164160.4071964454083.59280355459228
72164169.611598706644-5.61159870664358
73168173.346368825837-5.346368825837
74173179.921105711391-6.92110571139114
75164163.7744304568260.225569543173833
76165165.823052935499-0.823052935498822
77205209.226785901903-4.22678590190284
78207201.3887141605935.61128583940683
79215208.4300033503386.5699966496615
80190178.21572443912211.7842755608785
81169171.021462214153-2.02146221415273
82175168.1097141857536.89028581424708
83188182.0103310400535.98966895994653
84188189.033257888467-1.03325788846652
85196196.448183339317-0.448183339317040
86201206.546299973469-5.54629997346905
87194192.4831848740361.51681512596366
88197195.0104817497471.98951825025298
89237246.507635701937-9.50763570193737
90236239.313466768335-3.31346676833502
91244241.9814393520662.01856064793424
92222206.7996019473515.2003980526502
93195193.0481495206511.95185047934939
94199196.2954227925572.70457720744298
95207208.467525120273-1.46752512027308
96204208.164704095828-4.16470409582845
97212214.661651522177-2.66165152217744
98222221.8974011948900.10259880510975
99214213.1382301074850.861769892514872
100217215.5516771571621.44832284283794
101258266.180957549843-8.18095754984313
102256262.297655250605-6.29765525060452
103251265.966797634245-14.9667976342448
104223224.309114938151-1.30911493815077
105198195.0728156105042.92718438949615
106206199.0807991116616.91920088833854
107214212.0127446602101.98725533978958
108212212.431008420139-0.431008420138539
109227221.9790804050855.02091959491511
110238235.3299199062292.67008009377139
111228227.7027359634540.297264036545982
112235230.0595367862224.94046321377769
113275281.870930309566-6.87093030956606
114278279.503066021618-1.50306602161754
115278282.328962909445-4.32896290944456
116251249.3574581061181.64254189388222
117225220.2573628977084.74263710229155
118232227.359534053414.6404659465901
119238237.6252458163830.374754183617227
120239235.8240671545343.17593284546595







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121251.1088672358240.52074376064261.69699071096
122261.464424671384249.070684296064273.858165046704
123250.203866503083236.587899360919263.819833645247
124254.614317446025239.510934443462269.717700448589
125302.133271215603283.957250309501320.309292121705
126306.290578728036286.870341332535325.710816123537
127308.955498146876288.403364221524329.507632072229
128277.805810956971257.919400928858297.692220985084
129245.87418933481226.758238921605264.990139748015
130250.464546900181230.061061653823270.868032146540
131256.615329917521234.853633299169278.377026535872
132255.597555892736234.521485435768276.673626349703

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 251.1088672358 & 240.52074376064 & 261.69699071096 \tabularnewline
122 & 261.464424671384 & 249.070684296064 & 273.858165046704 \tabularnewline
123 & 250.203866503083 & 236.587899360919 & 263.819833645247 \tabularnewline
124 & 254.614317446025 & 239.510934443462 & 269.717700448589 \tabularnewline
125 & 302.133271215603 & 283.957250309501 & 320.309292121705 \tabularnewline
126 & 306.290578728036 & 286.870341332535 & 325.710816123537 \tabularnewline
127 & 308.955498146876 & 288.403364221524 & 329.507632072229 \tabularnewline
128 & 277.805810956971 & 257.919400928858 & 297.692220985084 \tabularnewline
129 & 245.87418933481 & 226.758238921605 & 264.990139748015 \tabularnewline
130 & 250.464546900181 & 230.061061653823 & 270.868032146540 \tabularnewline
131 & 256.615329917521 & 234.853633299169 & 278.377026535872 \tabularnewline
132 & 255.597555892736 & 234.521485435768 & 276.673626349703 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78863&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]121[/C][C]251.1088672358[/C][C]240.52074376064[/C][C]261.69699071096[/C][/ROW]
[ROW][C]122[/C][C]261.464424671384[/C][C]249.070684296064[/C][C]273.858165046704[/C][/ROW]
[ROW][C]123[/C][C]250.203866503083[/C][C]236.587899360919[/C][C]263.819833645247[/C][/ROW]
[ROW][C]124[/C][C]254.614317446025[/C][C]239.510934443462[/C][C]269.717700448589[/C][/ROW]
[ROW][C]125[/C][C]302.133271215603[/C][C]283.957250309501[/C][C]320.309292121705[/C][/ROW]
[ROW][C]126[/C][C]306.290578728036[/C][C]286.870341332535[/C][C]325.710816123537[/C][/ROW]
[ROW][C]127[/C][C]308.955498146876[/C][C]288.403364221524[/C][C]329.507632072229[/C][/ROW]
[ROW][C]128[/C][C]277.805810956971[/C][C]257.919400928858[/C][C]297.692220985084[/C][/ROW]
[ROW][C]129[/C][C]245.87418933481[/C][C]226.758238921605[/C][C]264.990139748015[/C][/ROW]
[ROW][C]130[/C][C]250.464546900181[/C][C]230.061061653823[/C][C]270.868032146540[/C][/ROW]
[ROW][C]131[/C][C]256.615329917521[/C][C]234.853633299169[/C][C]278.377026535872[/C][/ROW]
[ROW][C]132[/C][C]255.597555892736[/C][C]234.521485435768[/C][C]276.673626349703[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78863&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78863&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121251.1088672358240.52074376064261.69699071096
122261.464424671384249.070684296064273.858165046704
123250.203866503083236.587899360919263.819833645247
124254.614317446025239.510934443462269.717700448589
125302.133271215603283.957250309501320.309292121705
126306.290578728036286.870341332535325.710816123537
127308.955498146876288.403364221524329.507632072229
128277.805810956971257.919400928858297.692220985084
129245.87418933481226.758238921605264.990139748015
130250.464546900181230.061061653823270.868032146540
131256.615329917521234.853633299169278.377026535872
132255.597555892736234.521485435768276.673626349703



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')